Lucid dreams is a phrase to describe the state of someone knowing that they are dreaming. What I am looking for is a single word that describes that moment of realization. A friend suggested lucidity, but its definition doesn't quite fit right for what I am seeking.

This is the perfect fit. I selected this as the answer because, as defined in Merriam-Webster and other sources, it describes the point at which a person not only gains recognition of their identity, but also their situation. Bravo and excellent research. For extra credit, what would the proper, or otherwise creative uses of this term be? 'I reached a point of anagnorisis.', 'I anagnorisized and I was not longer disturbed by the unfolding events.', 'The best lucid dreams occur when I reach anagnorisis early on.', etc.
–
Wayne HartmanApr 21 '11 at 0:06

I am not sure how specialized moments of realization are in English. Using words that just mean that (in varied forms):

realization

discovery

awakening

aware

epiphany

eureka

click — "And then it clicked: I was dreaming!"

I am unable to think of a word that is reserved for a special subject of realization. Different terms have their typical uses but I think the emotional feeling or suddenness is more of a deciding factor.

The first moment of realization of a lucid dream is, to me, not unlike a feeling of rebirth. So, I think it would be appropriate to describe the sensation using a word which means "the first movements of a fetus."